Show live online-players count on the home screen

- OnlineService.getOnlineCount(); mock random-walks a believable number,
  SignalrService reads GET /api/stats/online (server tracks hub connections)
- Home screen badge with pulsing dot, polls every 8s, localized digits

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/lib/online/mock-service.ts

@@ -737,6 +737,14 @@ export class MockOnlineService implements OnlineService {
 
   /* --------------------- leaderboard / shop / daily ------------------ */
 
+  private onlineCount = 600 + Math.floor(Math.random() * 900);
+  async getOnlineCount(): Promise<number> {
+    // gentle random walk so the badge feels alive
+    this.onlineCount += Math.round((Math.random() - 0.5) * 40);
+    this.onlineCount = Math.max(120, Math.min(6000, this.onlineCount));
+    return this.onlineCount;
+  }
+
   async getLeaderboard(): Promise<LeaderboardEntry[]> {
     const p = await this.getProfile();
     const others = Array.from({ length: 24 }, () => ({